arXiv subjects
Publications and source records attributed to Silvia Brannetti.
Let $α_X^{\underline d}$ be the Abel map of multidegree $\underline d$ of a singular curve $X$ of genus $g$. We describe the closure of ${\rm Im}α_X^{\underline d}$ inside Caporaso's compactified Jacobian $\bar{P_X^d}$ for irreducible curves, curves of compact type and binary curves.
We construct the moduli spaces of tropical curves and tropical principally polarized abelian varieties, working in the category of (what we call) stacky fans. We define the tropical Torelli map between these two moduli spaces and we study the fibers (tropical Torelli theorem) and the image of this map (tropical Schottky problem). Finally we determine the image of the planar tropical curves via the tropical Torelli map and we use it to give a positive answer to a question raised by Namikawa on the compactified classical Torelli map.
We give some results on quadratic normality of reducible curves canonically embedded and partially extend this study to their projective normality.
We present an alternative proof of the Alexander-Hirschowitz Theorem in dimension 3 using degenerations of toric varieties.